Level statistics for nearly integrable systems

TL;DR

This paper develops analytical models for the spectral statistics of quantum systems transitioning from integrability to chaos, using superpositions of independent random matrix ensembles, and validates them with microwave billiard data.

Contribution

It introduces a new analytical framework for level statistics in nearly integrable systems based on superpositions of random matrix spectra.

Findings

Analytical expressions for level spacing distribution derived.

Level number variance formulas obtained.

Model successfully applied to microwave billiard spectra.

Abstract

We assume that the level spectra of quantum systems in the initial phase of transition from integrability to chaos are approximated by superpositions of independent sequences. Each individual sequence is modeled by a random matrix ensemble. We obtain analytical expressions for the level spacing distribution and level number variance for such a system. These expressions are successfully applied to the analysis of the resonance spectrum in a nearly integrable microwave billiard.